Initial Code
#Read dataset
#Dataset with outliers
BostonCondo_OT <- read.csv("Boston_Condo_w_Outliers.csv", stringsAsFactors = F)
#Dataset without outliers
BostonCondo_No_OT <- read.csv("Boston_Condo_no_Outliers.csv", stringsAsFactors = F)
BostonCondo_OT <- BostonCondo_OT[,-1]
BostonCondo_No_OT <- BostonCondo_No_OT[,-1]
BostonCondo_OT$ZIPCODE <-as.character(BostonCondo_OT$ZIPCODE)
BostonCondo_No_OT$ZIPCODE <- as.character(BostonCondo_No_OT$ZIPCODE)str(BostonCondo_OT)## 'data.frame': 65198 obs. of 25 variables:
## $ ZIPCODE : chr "2128" "2128" "2128" "2110" ...
## $ OWN_OCC : chr "Y" "Y" "N" "N" ...
## $ AV_BLDG : int 364700 373400 394400 639100 690200 956800 790900 606400 547100 380800 ...
## $ YR_BUILT : int 1900 1900 1900 1972 1972 1972 1972 1972 1972 1960 ...
## $ YR_REMOD : int 2018 2018 2018 0 1977 2005 0 2017 0 2009 ...
## $ GROSS_AREA : int 791 799 908 744 868 1636 1210 880 756 952 ...
## $ NUM_FLOORS : num 1 1 1 1 1 1 1 1 1 2 ...
## $ U_BASE_FLOOR : int 1 2 3 7 7 7 7 7 8 1 ...
## $ U_NUM_PARK : int 0 0 0 0 1 0 0 0 0 1 ...
## $ U_CORNER : chr "N - No" "N - No" "N - No" "N - No" ...
## $ U_ORIENT : chr "T - Through" "T - Through" "T - Through" "T - Through" ...
## $ U_BDRMS : int 2 3 3 2 1 2 2 1 1 2 ...
## $ U_FULL_BTH : int 1 1 1 1 1 2 1 1 1 1 ...
## $ U_HALF_BTH : int 0 0 0 0 0 1 1 0 0 0 ...
## $ U_BTH_STYLE : chr "M - Modern" "M - Modern" "M - Modern" "L - Luxury" ...
## $ U_BTH_STYLE2 : chr "No" "No" "No" "No" ...
## $ U_BTH_STYLE3 : chr "No" "No" "No" "No" ...
## $ U_KITCH_TYPE : chr "F - Full Eat In" "F - Full Eat In" "F - Full Eat In" "O - One Person" ...
## $ U_KITCH_STYLE: chr "M - Modern" "M - Modern" "M - Modern" "L - Luxury" ...
## $ U_HEAT_TYP : chr "W - Ht Water/Steam" "W - Ht Water/Steam" "W - Ht Water/Steam" "W - Ht Water/Steam" ...
## $ U_AC : chr "N - None" "N - None" "N - None" "C - Central AC" ...
## $ U_FPLACE : int 0 0 0 0 0 0 0 0 0 0 ...
## $ U_INT_FIN : chr "N - Normal" "N - Normal" "N - Normal" "N - Normal" ...
## $ U_INT_CND : chr "G - Good" "G - Good" "G - Good" "E - Excellent" ...
## $ U_VIEW : chr "A - Average" "A - Average" "A - Average" "G - Good" ...str(BostonCondo_No_OT)## 'data.frame': 58105 obs. of 25 variables:
## $ ZIPCODE : chr "2128" "2128" "2128" "2110" ...
## $ OWN_OCC : chr "Y" "Y" "N" "N" ...
## $ AV_BLDG : int 364700 373400 394400 639100 690200 956800 790900 606400 547100 380800 ...
## $ YR_BUILT : int 1900 1900 1900 1972 1972 1972 1972 1972 1972 1960 ...
## $ YR_REMOD : int 2018 2018 2018 0 1977 2005 0 2017 0 2009 ...
## $ GROSS_AREA : int 791 799 908 744 868 1636 1210 880 756 952 ...
## $ NUM_FLOORS : num 1 1 1 1 1 1 1 1 1 2 ...
## $ U_BASE_FLOOR : int 1 2 3 7 7 7 7 7 8 1 ...
## $ U_NUM_PARK : int 0 0 0 0 1 0 0 0 0 1 ...
## $ U_CORNER : chr "N - No" "N - No" "N - No" "N - No" ...
## $ U_ORIENT : chr "T - Through" "T - Through" "T - Through" "T - Through" ...
## $ U_BDRMS : int 2 3 3 2 1 2 2 1 1 2 ...
## $ U_FULL_BTH : int 1 1 1 1 1 2 1 1 1 1 ...
## $ U_HALF_BTH : int 0 0 0 0 0 1 1 0 0 0 ...
## $ U_BTH_STYLE : chr "M - Modern" "M - Modern" "M - Modern" "L - Luxury" ...
## $ U_BTH_STYLE2 : chr "No" "No" "No" "No" ...
## $ U_BTH_STYLE3 : chr "No" "No" "No" "No" ...
## $ U_KITCH_TYPE : chr "F - Full Eat In" "F - Full Eat In" "F - Full Eat In" "O - One Person" ...
## $ U_KITCH_STYLE: chr "M - Modern" "M - Modern" "M - Modern" "L - Luxury" ...
## $ U_HEAT_TYP : chr "W - Ht Water/Steam" "W - Ht Water/Steam" "W - Ht Water/Steam" "W - Ht Water/Steam" ...
## $ U_AC : chr "N - None" "N - None" "N - None" "C - Central AC" ...
## $ U_FPLACE : int 0 0 0 0 0 0 0 0 0 0 ...
## $ U_INT_FIN : chr "N - Normal" "N - Normal" "N - Normal" "N - Normal" ...
## $ U_INT_CND : chr "G - Good" "G - Good" "G - Good" "E - Excellent" ...
## $ U_VIEW : chr "A - Average" "A - Average" "A - Average" "G - Good" ...library(caret)## Loading required package: lattice## Loading required package: ggplot2Scenario 1: With outliers
#Split the dataset into training and testing (90% Training, 10% Testing)
#folds1 <- createFolds(BostonCondo_OT$AV_BLDG)
#
#for (f in folds1){
# train1 <- BostonCondo_OT[-f,]
# test1 <- BostonCondo_OT[f,]
#}#save training & testing dataset
#write.csv(train1, "train1.csv")
#wirte.csv(test1, "test1.csv")#Read dataset
train1 <- read.csv("train1.csv", stringsAsFactors = F)
test1 <- read.csv("test1.csv", stringsAsFactors = F)
train1 <- train1[,-1]
test1 <- test1[,-1]
train1$ZIPCODE <-as.character(train1$ZIPCODE)
test1$ZIPCODE <- as.character(test1$ZIPCODE)#multi linear regression - 5 fold cross validation
startime <- Sys.time()
control1_1 <- trainControl(method="cv", number = 10)
mlr1 <- train(AV_BLDG~., data = train1, method ="lm", trControl=control1_1)## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleadingendtime <- Sys.time()
endtime - startime## Time difference of 18.07396 secsmlr1## Linear Regression
##
## 58678 samples
## 24 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 52810, 52810, 52810, 52811, 52811, 52811, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 339103.4 0.8028159 177918.2
##
## Tuning parameter 'intercept' was held constant at a value of TRUEsummary(mlr1)##
## Call:
## lm(formula = .outcome ~ ., data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12294752 -110577 15471 118242 23401773
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.016e+06 3.532e+05 5.708 1.15e-08 ***
## ZIPCODE2109 -1.702e+05 1.530e+04 -11.122 < 2e-16 ***
## ZIPCODE2110 -2.902e+05 1.540e+04 -18.848 < 2e-16 ***
## ZIPCODE2111 -3.277e+05 1.432e+04 -22.883 < 2e-16 ***
## ZIPCODE2113 -2.211e+05 1.534e+04 -14.411 < 2e-16 ***
## ZIPCODE2114 -1.920e+05 1.301e+04 -14.764 < 2e-16 ***
## ZIPCODE2115 -1.474e+05 1.287e+04 -11.454 < 2e-16 ***
## ZIPCODE2116 -1.792e+03 1.188e+04 -0.151 0.880121
## ZIPCODE2118 -1.531e+05 1.242e+04 -12.320 < 2e-16 ***
## ZIPCODE2119 -6.929e+05 1.632e+04 -42.448 < 2e-16 ***
## ZIPCODE2120 -5.858e+05 2.090e+04 -28.035 < 2e-16 ***
## ZIPCODE2121 -7.138e+05 2.144e+04 -33.294 < 2e-16 ***
## ZIPCODE2122 -7.012e+05 1.500e+04 -46.746 < 2e-16 ***
## ZIPCODE2124 -7.094e+05 1.504e+04 -47.163 < 2e-16 ***
## ZIPCODE2125 -6.241e+05 1.429e+04 -43.661 < 2e-16 ***
## ZIPCODE2126 -6.897e+05 2.413e+04 -28.585 < 2e-16 ***
## ZIPCODE2127 -4.127e+05 1.226e+04 -33.672 < 2e-16 ***
## ZIPCODE2128 -5.327e+05 1.406e+04 -37.898 < 2e-16 ***
## ZIPCODE2129 -4.000e+05 1.286e+04 -31.109 < 2e-16 ***
## ZIPCODE2130 -6.188e+05 1.276e+04 -48.508 < 2e-16 ***
## ZIPCODE2131 -7.398e+05 1.455e+04 -50.835 < 2e-16 ***
## ZIPCODE2132 -6.654e+05 1.573e+04 -42.302 < 2e-16 ***
## ZIPCODE2134 -4.702e+05 1.396e+04 -33.672 < 2e-16 ***
## ZIPCODE2135 -4.641e+05 1.254e+04 -37.010 < 2e-16 ***
## ZIPCODE2136 -7.854e+05 1.753e+04 -44.797 < 2e-16 ***
## ZIPCODE2199 2.944e+06 8.676e+04 33.938 < 2e-16 ***
## ZIPCODE2210 -1.576e+05 1.712e+04 -9.206 < 2e-16 ***
## ZIPCODE2215 -2.113e+05 1.331e+04 -15.880 < 2e-16 ***
## ZIPCODE2446 -7.540e+05 2.411e+05 -3.127 0.001766 **
## ZIPCODE2467 -7.703e+05 1.753e+04 -43.952 < 2e-16 ***
## OWN_OCCY -2.536e+04 3.032e+03 -8.367 < 2e-16 ***
## YR_BUILT -6.186e+02 4.621e+01 -13.387 < 2e-16 ***
## YR_REMOD 4.690e+00 2.068e+00 2.268 0.023329 *
## GROSS_AREA 7.639e+02 4.781e+00 159.777 < 2e-16 ***
## NUM_FLOORS -1.664e+05 3.328e+03 -49.982 < 2e-16 ***
## U_BASE_FLOOR -1.741e+03 5.022e+02 -3.467 0.000526 ***
## U_NUM_PARK 3.930e+04 2.573e+03 15.271 < 2e-16 ***
## `U_CORNERY - Yes` 4.794e+04 3.940e+03 12.167 < 2e-16 ***
## `U_ORIENTB - Rear Below` -1.759e+04 1.176e+04 -1.496 0.134579
## `U_ORIENTC - Courtyard` -1.435e+04 9.630e+03 -1.490 0.136197
## `U_ORIENTE - End` -1.629e+04 3.081e+04 -0.529 0.596893
## `U_ORIENTF - Front/Street` -2.361e+04 4.748e+03 -4.973 6.62e-07 ***
## `U_ORIENTM - Middle` 1.434e+04 8.638e+03 1.660 0.096897 .
## `U_ORIENTT - Through` 1.461e+03 4.816e+03 0.303 0.761593
## U_BDRMS -4.568e+04 2.547e+03 -17.937 < 2e-16 ***
## U_FULL_BTH 3.456e+05 6.989e+03 49.441 < 2e-16 ***
## U_HALF_BTH 3.268e+05 7.760e+03 42.107 < 2e-16 ***
## `U_BTH_STYLEM - Modern` -1.495e+05 1.076e+04 -13.889 < 2e-16 ***
## `U_BTH_STYLEN - No Remodeling` -1.346e+05 1.854e+04 -7.261 3.88e-13 ***
## `U_BTH_STYLES - Semi-Modern` -1.484e+05 1.227e+04 -12.095 < 2e-16 ***
## `U_BTH_STYLE2M - Modern` -2.351e+03 1.300e+04 -0.181 0.856452
## `U_BTH_STYLE2N - No Remodeling` -7.496e+04 2.758e+04 -2.718 0.006578 **
## U_BTH_STYLE2No 3.350e+05 1.442e+04 23.240 < 2e-16 ***
## `U_BTH_STYLE2S - Semi-Modern` -6.306e+04 1.408e+04 -4.480 7.49e-06 ***
## `U_BTH_STYLE3M - Modern` -5.379e+05 1.579e+04 -34.060 < 2e-16 ***
## `U_BTH_STYLE3N - No Remodeling` -4.993e+05 4.939e+04 -10.109 < 2e-16 ***
## U_BTH_STYLE3No -3.384e+05 1.697e+04 -19.946 < 2e-16 ***
## `U_BTH_STYLE3S - Semi-Modern` -6.664e+05 1.874e+04 -35.563 < 2e-16 ***
## `U_KITCH_TYPEF - Full Eat In` -6.907e+04 3.407e+05 -0.203 0.839326
## `U_KITCH_TYPEN - None` -2.103e+05 3.424e+05 -0.614 0.539202
## `U_KITCH_TYPEO - One Person` -9.831e+04 3.407e+05 -0.289 0.772897
## `U_KITCH_TYPEP - Pullman` -1.209e+05 3.407e+05 -0.355 0.722736
## `U_KITCH_STYLEM - Modern` -9.153e+04 9.522e+03 -9.613 < 2e-16 ***
## `U_KITCH_STYLEN - No Remodeling` -1.371e+05 1.796e+04 -7.634 2.31e-14 ***
## `U_KITCH_STYLES - Semi-Modern` -1.147e+05 1.111e+04 -10.322 < 2e-16 ***
## `U_HEAT_TYPF - Forced Hot Air` -2.542e+04 6.323e+03 -4.021 5.81e-05 ***
## `U_HEAT_TYPN - None` -9.535e+05 1.720e+05 -5.543 2.98e-08 ***
## `U_HEAT_TYPO - Other` 4.283e+05 9.135e+04 4.688 2.76e-06 ***
## `U_HEAT_TYPP - Heat Pump` -2.152e+04 8.387e+03 -2.566 0.010288 *
## `U_HEAT_TYPS - Space Heat` -6.625e+03 3.853e+04 -0.172 0.863491
## `U_HEAT_TYPW - Ht Water/Steam` -4.602e+04 5.856e+03 -7.859 3.94e-15 ***
## `U_ACD - Ductless AC` 1.645e+04 2.390e+04 0.688 0.491260
## `U_ACN - None` 1.645e+04 4.286e+03 3.838 0.000124 ***
## U_FPLACE 6.332e+04 2.893e+03 21.886 < 2e-16 ***
## `U_INT_FING - Good` -3.577e+05 1.395e+05 -2.564 0.010348 *
## `U_INT_FINN - Normal` -3.555e+05 8.434e+03 -42.154 < 2e-16 ***
## `U_INT_FINS - Substandard` -3.944e+05 5.006e+04 -7.879 3.37e-15 ***
## `U_INT_CNDE - Excellent` 9.724e+04 7.245e+03 13.420 < 2e-16 ***
## `U_INT_CNDF - Fair` -3.675e+04 2.497e+04 -1.472 0.141047
## `U_INT_CNDG - Good` -3.797e+03 4.352e+03 -0.872 0.383016
## `U_INT_CNDP - Poor` -1.319e+05 7.326e+04 -1.800 0.071815 .
## `U_VIEWE - Excellent` 3.426e+05 8.502e+03 40.297 < 2e-16 ***
## `U_VIEWF - Fair` -4.322e+04 7.232e+03 -5.976 2.30e-09 ***
## `U_VIEWG - Good` 4.133e+04 4.526e+03 9.132 < 2e-16 ***
## `U_VIEWP - Poor` -1.673e+05 2.657e+04 -6.296 3.07e-10 ***
## `U_VIEWS - Special` 1.605e+06 2.769e+04 57.948 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 340500 on 58592 degrees of freedom
## Multiple R-squared: 0.8016, Adjusted R-squared: 0.8013
## F-statistic: 2785 on 85 and 58592 DF, p-value: < 2.2e-16predict_mlr1 <- predict(mlr1, test1)#Calculate the performance metrics for the prediction on testing set
# R2 is R-Squared. It measures how much the variance in the dependent variable which is explained by the model
# RMSE is root mean squared error. It measures the standard deviation of residuals
#MAE is Mean absolute error, the average of the absolute difference between the actual and predicted values in the dataset. It measures the average of the residuals in the dataset
data.frame( R2_1_1 = R2(predict_mlr1, test1$AV_BLDG),
RMSE_1_1 = RMSE(predict_mlr1, test1$AV_BLDG),
MAE_1_1 = MAE(predict_mlr1, test1$AV_BLDG))## R2_1_1 RMSE_1_1 MAE_1_1
## 1 0.7816596 350471.3 178332.3x= 1:length(test1$AV_BLDG)
plot(x, test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment - Actual Value")
plot(x, predict_mlr1, col='blue', ylab = "Value", type="p", main="Boston Condo Property Assessment - Predicted Value")
plot(x, test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment")
par(new=T)
plot(x, predict_mlr1, col='blue', ylab = "", type="p")
legend("topright", legend=c("Actual Value", "Predicted Value"), fill = c("red","blue"), col=2:3, adj=c(0,0.6))
grid()
plot(predict_mlr1, test1$AV_BLDG, xlab = "preidtced value", ylab = "actual value")
abline(a=0,b=1)
library(randomForest)## randomForest 4.6-14## Type rfNews() to see new features/changes/bug fixes.##
## Attaching package: 'randomForest'## The following object is masked from 'package:ggplot2':
##
## margin#random forest with 5 trees
startime <- Sys.time()
control1_2 <- trainControl(method="cv", number = 10, search = "grid")
rf1_1 <- train(AV_BLDG~., data = train1, method ="rf", ntree=5, trControl=control1_2)
endtime <- Sys.time()
endtime - startime## Time difference of 23.68411 minsrf1_1## Random Forest
##
## 58678 samples
## 24 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 52810, 52810, 52810, 52810, 52810, 52811, ...
## Resampling results across tuning parameters:
##
## mtry RMSE Rsquared MAE
## 2 450899.2 0.7080347 210605.40
## 43 223102.4 0.9138811 78101.69
## 85 220741.8 0.9162428 76171.78
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was mtry = 85.plot(rf1_1)
#preidct on test set
predict_rf1_1 <- predict(rf1_1, test1)#Show performance metrics on test set
data.frame( R2_1_2 = R2(predict_rf1_1, test1$AV_BLDG),
RMSE_1_2 = RMSE(predict_rf1_1, test1$AV_BLDG),
MAE_1_2 = MAE(predict_rf1_1, test1$AV_BLDG))## R2_1_2 RMSE_1_2 MAE_1_2
## 1 0.9243845 205950.6 75942.36#visualize the results of actual value and predicted value
x= 1:length(test1$AV_BLDG)
plot(x, test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment - Actual Value")
plot(x, predict_rf1_1, col='blue', ylab = "Value", type="p", main="Boston Condo Property Assessment - Predicted Value")
plot(x, test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment")
par(new=T)
plot(x, predict_rf1_1, col='blue', ylab = "", type="p")
legend("topright", legend=c("Actual Value", "Predicted Value"), fill = c("red","blue"), col=2:3, adj=c(0,0.6))
grid()
#Visualize how close predicted value and actual value are
plot(predict_rf1_1, test1$AV_BLDG, xlab = "preidtced value", ylab = "actual value")
abline(a=0,b=1)
#random forest with 10 trees
startime <- Sys.time()
rf1_2 <- train(AV_BLDG~., data = train1, method ="rf", ntree=10, trControl=control1_2)
endtime <- Sys.time()
endtime - startime## Time difference of 46.81932 minsrf1_2## Random Forest
##
## 58678 samples
## 24 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 52810, 52811, 52810, 52811, 52810, 52810, ...
## Resampling results across tuning parameters:
##
## mtry RMSE Rsquared MAE
## 2 441245.2 0.7428750 201307.93
## 43 205585.3 0.9255190 72337.94
## 85 201065.4 0.9296036 71580.06
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was mtry = 85.plot(rf1_2)
predict_rf1_2 <- predict(rf1_2, test1)data.frame( R2_1_3 = R2(predict_rf1_2, test1$AV_BLDG),
RMSE_1_3 = RMSE(predict_rf1_2, test1$AV_BLDG),
MAE_1_3 = MAE(predict_rf1_2, test1$AV_BLDG))## R2_1_3 RMSE_1_3 MAE_1_3
## 1 0.9431407 179246.8 69571.51#visualize the results of actual value and predicted value
x= 1:length(test1$AV_BLDG)
plot(x, test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment - Actual Value")
plot(x, predict_rf1_2, col='blue', ylab = "Value", type="p", main="Boston Condo Property Assessment - Predicted Value")
plot(x, test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment")
par(new=T)
plot(x, predict_rf1_2, col='blue', ylab = "", type="p")
legend("topright", legend=c("Actual Value", "Predicted Value"), fill = c("red","blue"), col=2:3, adj=c(0,0.6))
grid()
#Visualize how close predicted value and actual value are
plot(predict_rf1_2, test1$AV_BLDG, xlab = "preidtced value", ylab = "actual value")
abline(a=0,b=1)
library(class)
library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:randomForest':
##
## combine## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union#prepare data for k nearest neighbor regression
x_train1 = train1
x_test1 = test1#onehot encoding
dmy1 <- dummyVars(" ~ .", data = x_train1)
x_train1 <- data.frame(predict(dmy1, newdata = x_train1))
dmy2 <- dummyVars(" ~ .", data = x_test1)
x_test1 <- data.frame(predict(dmy2, newdata = x_test1))#plug 0 value into attributes missing from test set after one hot encoding
x_test1$U_HEAT_TYPN...None <- 0
x_test1 <- x_test1 %>% relocate(U_HEAT_TYPN...None, .after = U_HEAT_TYPF...Forced.Hot.Air)#k nearest regression
startime <- Sys.time()
knn1 <- train(AV_BLDG~., data = x_train1, method ="knn", trControl=control1_1, tuneGrid = expand.grid(k=1:2))
endtime <- Sys.time()
endtime - startime## Time difference of 45.7329 minsknn1## k-Nearest Neighbors
##
## 58678 samples
## 99 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 52811, 52811, 52809, 52810, 52809, 52811, ...
## Resampling results across tuning parameters:
##
## k RMSE Rsquared MAE
## 1 528408.8 0.5844252 185982.8
## 2 470666.3 0.6367171 186668.5
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was k = 2.predict_knn1 <- predict(knn1, x_test1)data.frame( R2_1_4 = R2(predict_knn1, x_test1$AV_BLDG),
RMSE_1_4 = RMSE(predict_knn1, x_test1$AV_BLDG),
MAE_1_4 = MAE(predict_knn1, x_test1$AV_BLDG))## R2_1_4 RMSE_1_4 MAE_1_4
## 1 0.6155162 478633 184474.3x= 1:length(x_test1$AV_BLDG)
plot(x, x_test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment - Actual Value")
plot(x, predict_knn1, col='blue', ylab = "Value", type="p", main="Boston Condo Property Assessment - Predicted Value")
plot(x, x_test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment")
par(new=T)
plot(x, predict_knn1, col='blue', ylab = "", type="p")
legend("topright", legend=c("Actual Value", "Predicted Value"), fill = c("red","blue"), col=2:3, adj=c(0,0.6))
grid()
plot(predict_knn1, x_test1$AV_BLDG, xlab = "preidtced value", ylab = "actual value")
abline(a=0,b=1)
Scenario 2. Without Outliers in training set
#remove rows including outliers
train2 <- train1[train1$AV_BLDG %in% BostonCondo_No_OT$AV_BLDG,]#multi linear regression
startime <- Sys.time()
control2_1 <- trainControl(method="cv", number = 10)
mlr2 <- train(AV_BLDG~., data = train2, method ="lm", trControl=control2_1)## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleadingendtime <- Sys.time()
endtime - startime## Time difference of 14.07458 secsmlr2## Linear Regression
##
## 53351 samples
## 24 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 48015, 48017, 48016, 48015, 48015, 48015, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 117040.4 0.7851128 82314.91
##
## Tuning parameter 'intercept' was held constant at a value of TRUEsummary(mlr2)##
## Call:
## lm(formula = .outcome ~ ., data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1093968 -57642 4889 55915 816243
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.601e+06 1.238e+05 12.932 < 2e-16 ***
## ZIPCODE2109 -1.199e+05 6.207e+03 -19.312 < 2e-16 ***
## ZIPCODE2110 -8.627e+04 6.463e+03 -13.349 < 2e-16 ***
## ZIPCODE2111 -1.505e+05 5.858e+03 -25.693 < 2e-16 ***
## ZIPCODE2113 -1.634e+05 5.943e+03 -27.498 < 2e-16 ***
## ZIPCODE2114 -1.253e+05 5.262e+03 -23.810 < 2e-16 ***
## ZIPCODE2115 -1.137e+05 5.244e+03 -21.676 < 2e-16 ***
## ZIPCODE2116 -2.504e+04 5.024e+03 -4.984 6.26e-07 ***
## ZIPCODE2118 -8.073e+04 5.137e+03 -15.714 < 2e-16 ***
## ZIPCODE2119 -4.986e+05 6.258e+03 -79.679 < 2e-16 ***
## ZIPCODE2120 -4.365e+05 7.702e+03 -56.670 < 2e-16 ***
## ZIPCODE2121 -5.509e+05 7.858e+03 -70.100 < 2e-16 ***
## ZIPCODE2122 -5.096e+05 5.849e+03 -87.120 < 2e-16 ***
## ZIPCODE2124 -5.127e+05 5.862e+03 -87.455 < 2e-16 ***
## ZIPCODE2125 -4.474e+05 5.639e+03 -79.340 < 2e-16 ***
## ZIPCODE2126 -5.737e+05 8.748e+03 -65.581 < 2e-16 ***
## ZIPCODE2127 -2.642e+05 5.038e+03 -52.446 < 2e-16 ***
## ZIPCODE2128 -4.144e+05 5.554e+03 -74.606 < 2e-16 ***
## ZIPCODE2129 -2.256e+05 5.229e+03 -43.152 < 2e-16 ***
## ZIPCODE2130 -3.856e+05 5.190e+03 -74.292 < 2e-16 ***
## ZIPCODE2131 -5.252e+05 5.722e+03 -91.787 < 2e-16 ***
## ZIPCODE2132 -5.053e+05 6.060e+03 -83.384 < 2e-16 ***
## ZIPCODE2134 -3.519e+05 5.504e+03 -63.930 < 2e-16 ***
## ZIPCODE2135 -3.483e+05 5.090e+03 -68.427 < 2e-16 ***
## ZIPCODE2136 -5.968e+05 6.638e+03 -89.905 < 2e-16 ***
## ZIPCODE2199 -3.465e+05 1.170e+05 -2.963 0.003053 **
## ZIPCODE2210 -1.043e+05 7.424e+03 -14.055 < 2e-16 ***
## ZIPCODE2215 -1.493e+05 5.321e+03 -28.062 < 2e-16 ***
## ZIPCODE2446 -5.773e+05 8.279e+04 -6.973 3.15e-12 ***
## ZIPCODE2467 -4.399e+05 6.777e+03 -64.914 < 2e-16 ***
## OWN_OCCY 6.345e+03 1.096e+03 5.788 7.15e-09 ***
## YR_BUILT -3.458e+02 1.698e+01 -20.357 < 2e-16 ***
## YR_REMOD 5.876e+00 7.475e-01 7.861 3.89e-15 ***
## GROSS_AREA 2.561e+02 2.218e+00 115.503 < 2e-16 ***
## NUM_FLOORS -5.008e+04 1.304e+03 -38.412 < 2e-16 ***
## U_BASE_FLOOR -7.126e+02 2.173e+02 -3.279 0.001041 **
## U_NUM_PARK 2.265e+04 9.612e+02 23.563 < 2e-16 ***
## `U_CORNERY - Yes` 2.158e+04 1.440e+03 14.994 < 2e-16 ***
## `U_ORIENTB - Rear Below` -3.738e+04 4.100e+03 -9.116 < 2e-16 ***
## `U_ORIENTC - Courtyard` -1.203e+04 3.404e+03 -3.535 0.000409 ***
## `U_ORIENTE - End` -3.190e+04 1.131e+04 -2.821 0.004797 **
## `U_ORIENTF - Front/Street` 3.466e+03 1.703e+03 2.035 0.041857 *
## `U_ORIENTM - Middle` 1.009e+04 3.093e+03 3.263 0.001102 **
## `U_ORIENTT - Through` -5.735e+03 1.725e+03 -3.325 0.000885 ***
## U_BDRMS 1.590e+04 9.447e+02 16.836 < 2e-16 ***
## U_FULL_BTH 1.378e+04 3.648e+03 3.778 0.000158 ***
## U_HALF_BTH 2.857e+03 3.862e+03 0.740 0.459415
## `U_BTH_STYLEM - Modern` -6.018e+04 4.606e+03 -13.068 < 2e-16 ***
## `U_BTH_STYLEN - No Remodeling` -7.193e+04 7.009e+03 -10.263 < 2e-16 ***
## `U_BTH_STYLES - Semi-Modern` -6.394e+04 5.052e+03 -12.656 < 2e-16 ***
## `U_BTH_STYLE2M - Modern` -5.547e+04 6.879e+03 -8.063 7.60e-16 ***
## `U_BTH_STYLE2N - No Remodeling` -2.452e+04 1.147e+04 -2.137 0.032618 *
## U_BTH_STYLE2No -1.403e+05 7.694e+03 -18.238 < 2e-16 ***
## `U_BTH_STYLE2S - Semi-Modern` -9.532e+04 7.108e+03 -13.410 < 2e-16 ***
## `U_BTH_STYLE3M - Modern` 1.433e+04 2.209e+04 0.649 0.516554
## `U_BTH_STYLE3N - No Remodeling` 3.426e+04 3.291e+04 1.041 0.297865
## U_BTH_STYLE3No -1.071e+04 2.223e+04 -0.482 0.629993
## `U_BTH_STYLE3S - Semi-Modern` -7.687e+03 2.243e+04 -0.343 0.731823
## `U_KITCH_TYPEF - Full Eat In` -9.056e+04 1.169e+05 -0.775 0.438574
## `U_KITCH_TYPEN - None` -1.199e+05 1.176e+05 -1.019 0.308001
## `U_KITCH_TYPEO - One Person` -1.014e+05 1.169e+05 -0.867 0.385824
## `U_KITCH_TYPEP - Pullman` -1.705e+05 1.169e+05 -1.458 0.144735
## `U_KITCH_STYLEM - Modern` -4.656e+04 3.921e+03 -11.874 < 2e-16 ***
## `U_KITCH_STYLEN - No Remodeling` -7.556e+04 6.622e+03 -11.410 < 2e-16 ***
## `U_KITCH_STYLES - Semi-Modern` -7.746e+04 4.419e+03 -17.531 < 2e-16 ***
## `U_HEAT_TYPF - Forced Hot Air` 1.491e+03 2.257e+03 0.661 0.508833
## `U_HEAT_TYPN - None` -2.320e+05 8.395e+04 -2.763 0.005730 **
## `U_HEAT_TYPO - Other` 2.316e+04 3.384e+04 0.684 0.493853
## `U_HEAT_TYPP - Heat Pump` 3.164e+04 3.091e+03 10.235 < 2e-16 ***
## `U_HEAT_TYPS - Space Heat` 5.957e+03 1.323e+04 0.450 0.652598
## `U_HEAT_TYPW - Ht Water/Steam` -2.768e+03 2.070e+03 -1.337 0.181182
## `U_ACD - Ductless AC` 2.871e+04 8.393e+03 3.421 0.000624 ***
## `U_ACN - None` -1.856e+04 1.544e+03 -12.024 < 2e-16 ***
## U_FPLACE 4.273e+04 1.167e+03 36.624 < 2e-16 ***
## `U_INT_FING - Good` -7.204e+04 4.798e+04 -1.501 0.133261
## `U_INT_FINN - Normal` -6.168e+04 4.207e+03 -14.663 < 2e-16 ***
## `U_INT_FINS - Substandard` -9.660e+04 1.747e+04 -5.529 3.23e-08 ***
## `U_INT_CNDE - Excellent` 9.353e+04 2.701e+03 34.631 < 2e-16 ***
## `U_INT_CNDF - Fair` -1.069e+04 8.703e+03 -1.228 0.219351
## `U_INT_CNDG - Good` 2.808e+04 1.526e+03 18.406 < 2e-16 ***
## `U_INT_CNDP - Poor` -8.698e+04 2.526e+04 -3.444 0.000573 ***
## `U_VIEWE - Excellent` 1.305e+05 3.771e+03 34.606 < 2e-16 ***
## `U_VIEWF - Fair` -2.880e+04 2.560e+03 -11.250 < 2e-16 ***
## `U_VIEWG - Good` 3.563e+04 1.700e+03 20.962 < 2e-16 ***
## `U_VIEWP - Poor` -1.008e+05 9.216e+03 -10.942 < 2e-16 ***
## `U_VIEWS - Special` 4.306e+05 5.856e+04 7.353 1.97e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 116800 on 53265 degrees of freedom
## Multiple R-squared: 0.7862, Adjusted R-squared: 0.7858
## F-statistic: 2304 on 85 and 53265 DF, p-value: < 2.2e-16predict_mlr2 <- predict(mlr2, test1)#Calculate the performance metrics for the prediction on testing set
# R2 is R-Squared. It measures how much the variance in the dependent variable which is explained by the model
# RMSE is root mean squared error. It measures the standard deviation of residuals
#MAE is Mean absolute error, the average of the absolute difference between the actual and predicted values in the dataset. It measures the average of the residuals in the dataset
data.frame( R2_2_1 = R2(predict_mlr2, test1$AV_BLDG),
RMSE_2_1 = RMSE(predict_mlr2, test1$AV_BLDG),
MAE_2_1 = MAE(predict_mlr2, test1$AV_BLDG))## R2_2_1 RMSE_2_1 MAE_2_1
## 1 0.6933966 523067.3 178474.2x= 1:length(test1$AV_BLDG)
plot(x, test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment - Actual Value")
plot(x, predict_mlr2, col='blue', ylab = "Value", type="p", main="Boston Condo Property Assessment - Predicted Value")
plot(x, test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment")
par(new=T)
plot(x, predict_mlr2, col='blue', ylab = "", type="p")
legend("topright", legend=c("Actual Value", "Predicted Value"), fill = c("red","blue"), col=2:3, adj=c(0,0.6))
grid()
plot(predict_mlr2, test1$AV_BLDG, xlab = "preidtced value", ylab = "actual value")
abline(a=0,b=1)
#random forest with 5 trees
startime <- Sys.time()
control2_2 <- trainControl(method="cv", number = 10, search = "grid")
rf2_1 <- train(AV_BLDG~., data = train2, method ="rf", ntree=5, trControl=control2_2)
endtime <- Sys.time()
endtime - startime## Time difference of 18.88791 minsrf2_1## Random Forest
##
## 53351 samples
## 24 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 48017, 48014, 48016, 48017, 48015, 48016, ...
## Resampling results across tuning parameters:
##
## mtry RMSE Rsquared MAE
## 2 170813.96 0.6033097 127967.04
## 43 87504.65 0.8800031 50908.86
## 85 87696.11 0.8792837 50002.42
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was mtry = 43.plot(rf2_1)
#preidct on test set
predict_rf2_1 <- predict(rf2_1, test1)#Show performance metrics on test set
data.frame( R2_2_2 = R2(predict_rf2_1, test1$AV_BLDG),
RMSE_2_2 = RMSE(predict_rf2_1, test1$AV_BLDG),
MAE_2_2 = MAE(predict_rf2_1, test1$AV_BLDG))## R2_2_2 RMSE_2_2 MAE_2_2
## 1 0.4714317 601895.9 165442.7#visualize the results of actual value and predicted value
x= 1:length(test1$AV_BLDG)
plot(x, test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment - Actual Value")
plot(x, predict_rf2_1, col='blue', ylab = "Value", type="p", main="Boston Condo Property Assessment - Predicted Value")
plot(x, test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment")
par(new=T)
plot(x, predict_rf2_1, col='blue', ylab = "", type="p")
legend("topright", legend=c("Actual Value", "Predicted Value"), fill = c("red","blue"), col=2:3, adj=c(0,0.6))
grid()
#Visualize how close predicted value and actual value are
plot(predict_rf2_1, test1$AV_BLDG, xlab = "preidtced value", ylab = "actual value")
abline(a=0,b=1)
#random forest with 10 trees
startime <- Sys.time()
rf2_2 <- train(AV_BLDG~., data = train2, method ="rf", ntree=10, trControl=control2_2)
endtime <- Sys.time()
endtime - startime## Time difference of 37.5271 minsrf2_2## Random Forest
##
## 53351 samples
## 24 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 48016, 48016, 48016, 48017, 48015, 48016, ...
## Resampling results across tuning parameters:
##
## mtry RMSE Rsquared MAE
## 2 164450.73 0.6603781 123552.10
## 43 82185.58 0.8947526 47315.97
## 85 83148.29 0.8917390 46983.77
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was mtry = 43.plot(rf2_2)
predict_rf2_2 <- predict(rf2_2, test1)data.frame( R2_2_3 = R2(predict_rf2_2, test1$AV_BLDG),
RMSE_2_3 = RMSE(predict_rf2_2, test1$AV_BLDG),
MAE_2_3 = MAE(predict_rf2_2, test1$AV_BLDG))## R2_2_3 RMSE_2_3 MAE_2_3
## 1 0.4378564 613487.3 165277.6#visualize the results of actual value and predicted value
x= 1:length(test1$AV_BLDG)
plot(x, test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment - Actual Value")
plot(x, predict_rf2_2, col='blue', ylab = "Value", type="p", main="Boston Condo Property Assessment - Predicted Value")
plot(x, test1$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment")
par(new=T)
plot(x, predict_rf2_2, col='blue', ylab = "", type="p")
legend("topright", legend=c("Actual Value", "Predicted Value"), fill = c("red","blue"), col=2:3, adj=c(0,0.6))
grid()
#Visualize how close predicted value and actual value are
plot(predict_rf2_2, test1$AV_BLDG, xlab = "preidtced value", ylab = "actual value")
abline(a=0,b=1)
#prepare data for k nearest neighbor regression
x_train2 = train2
x_test2 = test1#onehot encoding
dmy1 <- dummyVars(" ~ .", data = x_train2)
x_train2 <- data.frame(predict(dmy1, newdata = x_train2))
dmy2 <- dummyVars(" ~ .", data = x_test2)
x_test2 <- data.frame(predict(dmy2, newdata = x_test2))#plug 0 value into attributes missing from test set after one hot encoding
x_test2$U_HEAT_TYPN...None <- 0
x_test2 <- x_test1 %>% relocate(U_HEAT_TYPN...None, .after = U_HEAT_TYPF...Forced.Hot.Air)#k nearest regression
startime <- Sys.time()
knn2 <- train(AV_BLDG~., data = x_train1, method ="knn", trControl=control2_1, tuneGrid = expand.grid(k=1:2))
endtime <- Sys.time()
endtime - startime## Time difference of 41.88771 minsknn2## k-Nearest Neighbors
##
## 58678 samples
## 99 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 52810, 52810, 52810, 52810, 52811, 52810, ...
## Resampling results across tuning parameters:
##
## k RMSE Rsquared MAE
## 1 522472.0 0.5915549 184392.6
## 2 467377.5 0.6420443 185586.6
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was k = 2.predict_knn2 <- predict(knn2, x_test2)data.frame( R2_2_4 = R2(predict_knn2, x_test2$AV_BLDG),
RMSE_2_4 = RMSE(predict_knn2, x_test2$AV_BLDG),
MAE_2_4 = MAE(predict_knn2, x_test2$AV_BLDG))## R2_2_4 RMSE_2_4 MAE_2_4
## 1 0.6155162 478633 184474.3x= 1:length(x_test2$AV_BLDG)
plot(x, x_test2$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment - Actual Value")
plot(x, predict_knn2, col='blue', ylab = "Value", type="p", main="Boston Condo Property Assessment - Predicted Value")
plot(x, x_test2$AV_BLDG, col="red", ylab = "Value", type="p",main="Boston Condo Property Assessment")
par(new=T)
plot(x, predict_knn2, col='blue', ylab = "", type="p")
legend("topright", legend=c("Actual Value", "Predicted Value"), fill = c("red","blue"), col=2:3, adj=c(0,0.6))
grid()
plot(predict_knn2, x_test2$AV_BLDG, xlab = "preidtced value", ylab = "actual value")
abline(a=0,b=1)